Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-25T02:17:02.161Z Has data issue: false hasContentIssue false
  • English
  • Français

Composition operators between weighted Banach spaces of analytic functions

Part of: Special classes of linear operators Linear function spaces and their duals

Published online by Cambridge University Press:  09 April 2009

J. Bonet ,
P. Domański ,
M. Lindström  and
J. Taskinen
J. Bonet
Affiliation:
Dept. Matemática Aplicada Univ. Politécnica de ValenciaE-46071 ValenciaSpain e-mail: [email protected]
P. Domański
Affiliation:
Faculty of Matematics and Comp. Sci. A. Mickiewicz University, ul. Matejki 48/49 60-769 PoznańPoland e-mail: [email protected]
M. Lindström
Affiliation:
Department of Mathematics Åbo Akademi University, FIN-20500 ÅboFinland e-mail: [email protected]
J. Taskinen
Affiliation:
Department of Mathematics P. O. Box 4, FIN-00014University of HelsinkiFinland e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We characterize those analytic self-maps ϕ of the unit disc which generate bounded or compact composition operators Cϕ between given weighted Banach spaces H∞v or H0v of analytic functions with the weighted sup-norms. We characterize also those composition operators which are bounded or compact with respect to all reasonable weights v.

MSC classification

Secondary: 47B38: Operators on function spaces (general) 46E15: Banach spaces of continuous, differentiable or analytic functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 64 , Issue 1 , February 1998 , pp. 101 - 118
Copyright
Copyright © Australian Mathematical Society 1998

References

[BBT]Bierstedt, K. D., Bonet, J. and Taskinen, J., ‘Spaces of holomorphic functions with growth conditions and associated weights’, Studia Math. (to appear).Google Scholar
[BS]Bierstedt, K. D. and Summers, W. H., ‘Biduals of weighted Banach spaces of analytic functions’, J. Austral. Math. Soc. (Series A) 54 (1993), 70–79.CrossRefGoogle Scholar
[C]Conway, J., Functions of one complex variable (Springer, Berlin, 1978).CrossRefGoogle Scholar
[CM]Cowen, C., MacCluer, B., Composition operators on spaces of analytic functions (CRC Press, Boca Raton, 1995).Google Scholar
[DJT]Diestel, J., Jarchow, H. and Tonge, A., Absolutely summing operators, Cambridge Studies in Advanced Mathematics 43 (Cambridge University Press, Cambridge, 1995).CrossRefGoogle Scholar
[J]Jarchow, H., ‘Some functional analytic properties of composition operators’, Quaestiones Math. 18 (1995), 229–256.CrossRefGoogle Scholar
[L1]Lusky, W., ‘On the structure of H v0(D) and h v0(D)’, Math. Nachr. 159 (1992), 279–289.CrossRefGoogle Scholar
[L2]Lusky, W., ‘On weighted spaces of harmonic and holomorphic functions’, J. London Math. Soc. 51 (1995), 309–320.CrossRefGoogle Scholar
[Po]Pommerenke, Ch., Boundary behaviour of conformal maps, Grundlehren Math. Wiss. 299 (Springer, Berlin, 1992).CrossRefGoogle Scholar
[RS]Rubel, L. A., Shields, A. L., ‘The second duals of certain spaces of analytic functions’, J. Austral. Math. Soc. 11 (1970), 276–280.CrossRefGoogle Scholar
[Sh]Shapiro, J. H., Composition operators and classical function theory (Springer, Berlin, 1993).CrossRefGoogle Scholar
[SW1]Shields, A. L., Williams, D. L., ‘Bounded projections, duality, and multipliers in spaces of harmonic functions’, J. Reine Angew. Math. 299/300 (1978), 256–279.Google Scholar
[SW2]Shields, A. L., Williams, D. L., ‘Bounded projections and the growth of harmonic conjugates in the disk’, Michigan Math. J. 29 (1982), 3–25.CrossRefGoogle Scholar
[SS]Singh, R. K. and Summers, W. H., ‘Composition operators on weighted spaces of continuous functions’, J. Austral. Math. Soc. (Series A) 45 (1988), 303–319.CrossRefGoogle Scholar
[T]Taskinen, J., Compact composition operators on general weighted spaces, Department of Mathematics, Univ. Helsinki Preprint 121, 1996.Google Scholar
[Z]Zhu, K., Operator theory in function spaces (Dekker, New York, 1995).Google Scholar